Hello, and thanks for writing in.
I agree with Dr. Peter. While a foreign body lodged in the throat is possible, it's overall very unlikely to be the cause of the type of coughing you are describing. When dogs come in for coughing "like something is stuck in it's throat", I would say 99% of the time, it's due to tracheobronchitis (tracheal irritation or infection), and less likely other causes, including a foreign body. Also, even in off chance that it would actually be a foreign body lodged in the throat, other than sweeping your finger in the back of Bijou's mouth, there really is no way to remove something like that at home. Foreign material lodged in a dog's throat, esophagus, or trachea, typically needs to be removed under sedation, with long instruments, with endoscopy, or with surgery.
So, other than giving the Robitussin, Bijou would need to be examined by a veterinarian to determine the exact cause of the coughing, and especially if foreign material is lodged in Bijou's throat, esophagus, or trachea.
I hope this helps.